This thesis formulates the Generalised Gaussian Process Convolution Model (GGPCM), which is a generalisation of the Gaussian Process Convolution Model presented by Tobar et al. [2015b]. The GGPCM provides a theoretical framework for nonparametric kernel models of multidimensional signals defined on multidimensional input spaces. We show that the GGPCM generalises and connects existing work; most notably, we derive a dual formulation of the cross-spectral mixture kernel presented by Ulrich et al. [2015]. Finally, we use the GGPCM to develop the Deep Kernel Model, which presents a new network structure for unsupervised learning.